~ ON PROBABILITY. 51 
| years, &c. ; that for two lives at 17, 19, 21, or 23 years, &c.; that for three 
lives as a lease of 24, 27, 50, or 33 years, &c. ; and though this latter method 
is a little more plausible than the former, on account of the steward’s liberty 
% of choosing which of these proportions he pleases, yet I cannot see any ana- 
Soy logy that this bears to the reason of the thing. So that at best it is but only 
groping in the dark.” 
a 85. The old tables, to which Richards here alludes, are frequently referred 
wie in to in the treatises of that day, under the name of Eecroid’s Tables: the time 
iS hao at which their author lived was not even then accurately known, but is con- 
Jectured to have been about the time of Henry VIII.’s reign, as the interest 
ict ig 1 of money when they were compiled was rather more than 10 per cent. The 
wg slightly improved method which Richards mentions as then still in practice, 
i was suggested in an anonymous treatise entitled “Tables for renewing and 
i fa purchasing Leases of Lives,” first published at Cambridge about 1685. This 
yi Which is the book which is often cited as Newton's “ Treatise on Life Annuities,” 
: ifn but with which he was no otherwise concerned than as it bears his approbation 
2 low tog as Lucasian Professor on the title-page, which is couched in the following 
id, of which terms :—* The method of this book is correct, and the numbers computed 
(ae problem with sufficient accuracy, as I judge from re-calculating several of them.”* 
paces work There are no other traces that Newton meddled with this subject. In this 
{¢ and iners treatise Alcroid’s tables are said to have been calculated at 117 3s. 6-E-d. 
td, tis ook per cent. The tables which Richards published are calculated at different 
eautiful ana: rates, from 4 to 8 per cent., and are given for all ages, from five to five 
lumber have years on one life, and from ten to ten on two, and on three joint lives. 
cable for the Since that period the principal improvement of such tables has consisted in 
attention of more careful and extensive registers of deaths to furnish the requisite data, 
zt of annuie for their construction: the only addition to their theory has been in the 
seepiions, a suggestion, that such registers ought only to be considered as furnishing the 
ever may be results of a number of experiments : consequently, that the ratios given by 
fitien in an them ought not to be immediately employed as probabilities a priori, but 
used as in the theory given in page 87.4 An excellent account may be 
country from found of the authors who have treated of questions connected with annuities 
the edition in in the article MorraLITY, in the supplement to the * Encyclopaedia Britan- 
ft but curious nica.” 
ede. “In 86. The first tables of mortality were, in fact, formed by Dr. Halley from 
tas, formerly, the registers of Breslau in Silesia, and are given in the Transactions of the 
ables for that Royal Society for 1693, art. 1. The next author who treated of this 
value and m subject is William Kersebcom, who published at the Hague, in 1730, a tract, 
§ ears, the entitled, “ Eerste Verhandeling tot een Proeve om te weeten de probable 
ersion of one menigte des volks in de provintie van Hollandt en Westvrieslandt.” An 
5 And this account of this work is given by Mr. Eames in the Philosophical Transac- 
) ae were of tions for 1738. In 1742 Kerseboom published two other tracts upon the 
eases a0 same subject, an account of which is given by Mr. Van Rixtel in the Philo- 
wb but ib 8 sophical Transactions for 1743, Kerseboom s table of mortality was formed 
yee lives, from registers of many thousand life annuitants in Holland and West Fries- 
—_— land, which had been kept there from 125 to 130 years previous to the date 
ci of his publication. 
EE 87. M. Desparcieux published, in 1746, his “ Essai sur les Probabilités dela. 
: Durée de la Vie Humaine,” in which he gave several tables of mortality, 
constructed from the lists of nominees in the French tontines and from the 
* Methodus hujus libri recté se habet; numerique, ut ex quibusdam ad calculum revocatis, judico, satis 
exacté computaatur. Is, Newton, Math. Prof, Luc. ! 
+ When insurances on lives began to be established in the beginning of the last century, their true princi. 
ples were so little understood or acted upon, that every insurer, of whatever age he might be, paid the same 
premium, the only restriction being, that his life should lie between five and sixty Sg 
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